Question

Материальная точка массой m=3,7 кг совершает колебания по закону 0,2cos(2t+π/3),м. Чему равна полная энергия колебательного движения точки?

Answer 1

Ответ:

0.296 Дж

Объяснение:

x=0,2*cos(2*t+π/3)    m=3.7 кг      W=?

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Из уравнения A=0.2 м   ω=2 рад/с

W=m*v²/2=m*(ω*A)²/2=3.7*(2*0.2)²/2=0.296 Дж

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Answer 2

Calculation of Total Energy of Oscillating Point Mass

To calculate the total energy of the oscillating point mass, we need to consider both its kinetic energy and potential energy.

The equation for the displacement of the point mass as a function of time is given as:

x(t) = 0.2cos(2t + π/3) m Here, t represents time in seconds.

To calculate the kinetic energy, we need to find the velocity of the point mass. The velocity can be obtained by taking the derivative of the displacement equation with respect to time:

v(t) = -0.4sin(2t + π/3) m/s The kinetic energy (KE) of the point mass is given by the equation:

KE = (1/2)mv^2

Substituting the value of m and v(t) into the equation, we get:

KE = (1/2)(3.7 kg)(-0.4sin(2t + π/3))^2 J

To calculate the potential energy, we need to find the potential energy function. The potential energy (PE) of the point mass is given by the equation:

PE = (1/2)kx^2

where k is the spring constant and x is the displacement of the point mass.

In this case, the potential energy is zero because there is no spring involved in the oscillation.

Therefore, the total energy (E) of the oscillating point mass is equal to the kinetic energy:

E = KE = (1/2)(3.7 kg)(-0.4sin(2t + π/3))^2 J

Please note that the total energy of the oscillating point mass will vary with time due to the sinusoidal nature of the displacement and velocity functions.

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